Author: Tomas Casanovas Martinez
Date: 13:35:49 02/16/00
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On February 15, 2000 at 09:12:25, Shep wrote: >Hi all, > >I was trying to write this post earlier, but found a flaw in my calculations, so >here goes the fixed one: > >Suppose you want to play a match on two machines with PB and only have two >machines of different speed. (Obviously, just adjusting the time controls to >reflect the speed difference won't make it fair.) > >Assume that machine A is the faster one and that machine B is slower by a factor >of k>1. The natural impulse would be to give machine B k-times as much >reflection time. >For simplicity, let's assume that both machines predict precisely 50% of their >opponent's moves. Then the effective reflection times for both side are: > > R_a(k) = 1+k/2 > R_b(k) = k+1/2 > >Both reflection time functions are linear in k and intersect at k=1, thus it's >easy to see that > > R_a(k) < R_b(k) for all k>1 > >Thus > > l := R_b(k)/R_a(k) > 1 for all k>1 > >is the factor by which B's reflection time is too big to be fair. > >Consequently, to have a fair match, the multiplier for B's reflection time needs >to be k/l instead of k. >A quick calculation yields the final formula: > > m := k/l = (k^2+2k)/(2k+1) > >Thus, if machine B is given m-times the reflection time of machine A, the match >is fair (under the assumption that both sides predict 50% which is not precise, >but rather realistic - the final formula is slightly more complex for uneven >prediction rates). > >Example table: > > k m > -------- > 2 ~1.6 > 3 ~2.1 > 4 ~2.7 > 5 ~3.1 > 10 ~5.8 > >--- >Shep Shep, Although you will find a lot of answers to your proposal that point out the lack of scientist foundation of your comments, I appreciate very positively your attempt to solve a very common problem among computer chess players. I am sure my case is not unusual: I buy a new computer roughly every two and a half years, when the speed of the new is about twice the previous one. Currently I have three computers P.90, P.200 and P.400. I have no interest to buy another P.400 computer to be 'perfect' in my chess matches. I prefer to wait until a P.1000 will appear. In this context I do prefer a pragmatic -although probably imperfect- approach like yours than listening the voice of the 'perfectionists' simply telling : 'You are wrong', without offering any positive solution to a clear problem common to a lot of chess players... or perhaps am I the only one computer chess lover having three computers at different speeds?. ;-) . Tom.
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